Question: Simplify the following expression: $ q = -6 - \dfrac{4}{-7x - 7} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-7x - 7}{-7x - 7}$ $ \dfrac{-6}{1} \times \dfrac{-7x - 7}{-7x - 7} = \dfrac{42x + 42}{-7x - 7} $ Therefore $ q = \dfrac{42x + 42}{-7x - 7} - \dfrac{4}{-7x - 7} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{42x + 42 - 4 }{-7x - 7} $ Distribute the negative sign: $q = \dfrac{42x + 42 - 4}{-7x - 7}$ $q = \dfrac{42x + 38}{-7x - 7}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{-42x - 38}{7x + 7}$